In the News (Tue 31 Mar 15)

The Poissondistribution describes a wide range of phenomena in the sciences.

However, the important property of processes described by the Poissondistribution is that the SD is the square root of the total counts registered To illustrate, the table shows the results of counting our radioactivesample for different time intervals (with some artificial variability thrown in).

Bernoullidistribution: This is used to describe discrete outcomes in trials such as coin-flipping, dice throwing, or the number and probabilities of DNA base pair changes.

The binomialdistribution with parameters n and λ/n, i.e., the probability distribution of the number of successes in n trials, with probability λ/n of success on each trial, approaches the Poissondistribution with expected value &lambda; as n approaches infinity.

Poisson was born to modestly situated parents, and owed his career to the new scientific institutions created by the Revolution, which systematically sought and advanced students of promise.

Poisson's Law of Large Numbers (1835), a generalization of Bernoulli and an advance on de Moivre, was the direct inspiration for Quetelet, and determined the direction of what is called the Continental school of statistics.

This was the Poissondistribution, which predicts the pattern in which random events of very low probability occur in the course of a very large number of trials.

For temporallydistributed events, the Poissondistribution is the probability distribution of the number of events that would occur within a preset time, the Erlangdistribution is the probability distribution of the amount of time until the nth event.

Poisson was named deputy professor at the École Polytechnique in 1802, a position he held until 1806 when he was appointed to the professorship at the École Polytechnique which Fourier had vacated when he had been sent by Napoleon to Grenoble.

The Poissondistribution describes the probability that a random event will occur in a time or space interval under the conditions that the probability of the event occurring is very small, but the number of trials is very large so that the event actually occurs a few times.

Poisson never wished to occupy himself with two things at the same time; when, in the course of his labours, a research project crossed his mind that did not form any immediate connection with what he was doing at the time, he contented himself with writing a few words in his little wallet.

The poissondistribution is used to model rates, such as rabbits per acre, defects per unit, or arrivals per hour.

For a random variable to be poissondistributed, the probability of an occurrence in an interval must be proportional to the length of the interval, and the number of occurrences per interval must be independent.

The poissoncumulativedistribution function is simply the sum of the poisson probability density function from 0 to x.

The Poissondistribution is sometimes called a Poissonian, analagous to the term Gaussian for a Gauss or normal distribution.

The Poissondistribution can be derived as a limiting case to the binomialdistribution as the number of trials goes to infinity and the expected number of successes remains fixed.

For temporallydistributed events, the Poissondistribution is the probability distribution of the number of events that would occur within a preset time, the Erlangdistribution is the probability distribution of the amount of time until the nth event.

The Poissondistribution is used to model the number of events occurring within a given time interval.

Note that because this is a discretedistribution that is only defined for integer values of x, the percent point function is not smooth in the way the percent point function typically is for a continuousdistribution.

Most general purpose statistical software programs, including Dataplot, support at least some of the probability functions for the Poissondistribution.

The main differences between the poissondistribution and the binomialdistribution is that in the binomial all eligible phenomena are studied, whereas in the poissondistribution only the cases with a particular outcome are studied.

One assumption in this application of the poissondistribution is that the chance of having an accident is randomly distributed: every individual has an equal chance.

Mathematically this is expressed in the fact that the variance and the mean for the poissondistribution are equal.

Other common uses of Poisson are in Physics to model radioactive particle emission and in insurance companies to model accident rates.

www.statsdirect.com /help/distributions/pp.htm (310 words)

Poisson Distribution(Site not responding. Last check: )

Other phenomena that often follow a poissondistribution are death of infants, the number of misprints in a book, the number of customers arriving, and the number of activations of a geiger counter.

However, if we want to use the binomialdistribution we have to know both the number of people who make it safely from A to B, and the number of people who have an accident while driving from A to B, whereas the number of accidents is sufficient for applying the poissondistribution.

Thus, the poissondistribution is cheaper to use because the number of accidents is usually recorded by the police department, whereas the total number of drivers is not.

To determine this underlying distribution, it is common to fit the observed distribution to a theoretical distribution by comparing the frequencies observed in the data to the expected frequencies of the theoretical distribution (i.e., a Chi-square goodness of fit test).

The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibulldistribution of extreme events, and the Gompertz distribution.

The betadistribution arises from a transformation of the Fdistribution and is typically used to model the distribution of order statistics.

The appropriateness of the exponential and Poissondistributions, their linkage and their properties which lead to simple analytics, often escape our students as textbooks rarely provide empirical evidence to justify them.

Another example is Schmuland (2001), who uses the Poisson model to explain the phenomena of bursts in shark attacks and the scoring patterns of ice hockey legend Wayne Gretzky.

Based on his observation that the Poissondistribution provides a good fit for goals scored in ice hockey games, Berry (2000) assumes an exponentialdistribution for the times between goals to estimate the strategic time to “pull the goalie” when a team is down in a game.

ite.pubs.informs.org /Vol3No2/Chu/index.php (2484 words)

Poisson distribution(Site not responding. Last check: )

The poissondistribution is an appropriate model for count data.

The poissondistribution was derived by the french mathematician Poisson in 1837, and the first application was the describtion of the number of death by horse kicking in the prussian army (Bortkiewicz, 1898).

The poissondistribution is a mathematical rule that assigns probabilities to the number occurences.